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# Goals know how to expand the potential in series of

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Unformatted text preview: xpansion in multipoles ! Goals: ! * Know how to expand the potential in series of multipoles * Know how to calculate the multipole terms Lecture 15 Monday March 3, 2014 r 2 = ⇢ ✏0 The dipole moment of a single charge in space is 1. Zero in all space (and that makes sense) 2. Undeﬁned 3. Depends on the coordinate system 4. Q/R Quadrupole Moment Term Zh 3(~ · r0 )2 r~ i (rr0 )2 dq = (3x2 Zh 3(~ · r R R R r2 ) x02 dq + 3xy x0 y 0 dq + 3xz x0 z 0 dq ~ r 0 )2 02 (rr ) Z Z Z R R2 R 000 +3+ 3xzx0 y 00 z 0 dq + 3yz ry 0)z 0 dq 0+dq z 2 3yz2 ) yzz2 dq xy x dq + (3y 2 y 2 (3 + r i dq = R 2 02 R r ) x dq + 3xy 00 R x y dq + 3xz x0 z 0 dq R 00 R 02 R 00 2 2 +3xy x y dq + (3y r ) y dq + 3yz y z dq R 00 R 00 R 02 2 2 +3xz x z dq + 3yz y z dq + (3z r ) z dq (3x 2 Extra Slides...
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## This document was uploaded on 03/29/2014 for the course PHYS 4002.001 at Minnesota.

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